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Centripetal Force

Example: A centrifuge has a rotational speed of 11,000 rpm.

a. What is the centripetal acceleration $(a_{c})$ of a molecule situated a distance of 6 cm from the axis of rotation?

b. How does the acceleration from part a $(a_{c})$ compare with the acceleration due to gravity?

Known:

Unknown:

Draw a picture:

Convert units to standard form:

$w=11.000\ \frac{rotation}{min}\times\frac{1\ min}{60\ sec}\times\frac{2\pi\ radian}{rotation}=1152\ \frac{rad}{s}=w$

$r=0.06\ m$

Solve for velocity (speed):

$v_{t}=w\times r$

$1152\ \frac{rad}{s}\times 0.06\ m=69.12\ \frac{m}{s}$

Solve for acceleration $(a_{c})$ :

$a_{c}=\frac{v_{t}^{2}}{r}=\frac{(69.12\ \frac{m}{s})^{2}}{0.06\ m}=79,615\ \frac{m}{s^2}$

Compare to gravity:

$g=9.81\ \frac{m}{s^2}$

$a_{c}=79,615\ \frac{m}{s^2}$

$\frac{a_{c}}{g}\Rightarrow a_{c}=8115\ times\ larger\ than\ g$